R for Art Sundays
Strange Attractors: General 2D Map - Part 1
An R experiment to create images generated by the trajectory of a particle according to a strange attractor.
Made with Rcpp, tidyverse
Blog post explaining the experiment: Rcpp, Camarón de la Isla and the Beauty of Maths
Inspired by: Strange Attractors: Creating Patterns in Chaos, by Julien C. Sprott
library(Rcpp)
library(tidyverse)
opt <- theme(legend.position = "none",
panel.background = element_rect(fill="white", color="black"),
plot.background = element_rect(fill="white"),
axis.ticks = element_blank(),
panel.grid = element_blank(),
axis.title = element_blank(),
axis.text = element_blank())
cppFunction('DataFrame createTrajectory(int n, double x0, double y0,
double a1, double a2, double a3, double a4, double a5,
double a6, double a7, double a8, double a9, double a10,
double a11, double a12, double a13, double a14) {
// create the columns
NumericVector x(n);
NumericVector y(n);
x[0]=x0;
y[0]=y0;
for(int i = 1; i < n; ++i) {
x[i] = a1+a2*x[i-1]+ a3*y[i-1]+ a4*pow(fabs(x[i-1]), a5)+ a6*pow(fabs(y[i-1]), a7);
y[i] = a8+a9*x[i-1]+ a10*y[i-1]+ a11*pow(fabs(x[i-1]), a12)+ a13*pow(fabs(y[i-1]), a14);
}
// return a new data frame
return DataFrame::create(_["x"]= x, _["y"]= y);
}
')
a1 <- -0.6817
a2 <- -0.8025
a3 <- -0.8242
a4 <- -0.1381
a5 <- 0.6624
a6 <- 0.9451
a7 <- 1.0059
a8 <- -0.9718
a9 <- 0.7188
a10 <- -0.68170
a11 <- -0.68171
a12 <- -0.68172
a13 <- -0.68173
a14 <- -0.68174
df <- createTrajectory(10000000, 1, 1, a1, a2, a3, a4, a5, a6,
a7, a8, a9, a10, a11, a12, a13, a14)
mx <- quantile(df$x, probs = 0.05)
Mx <- quantile(df$x, probs = 0.95)
my <- quantile(df$y, probs = 0.05)
My <- quantile(df$y, probs = 0.95)
df %>% filter(x > mx, x < Mx, y > my, y < My) -> df
plot <- ggplot(df) +
geom_point(aes(x, y), shape=46, alpha=0.01, size=0, color="black") +
scale_x_continuous(expand = c(0,0))+
scale_y_continuous(expand = c(0,0))+
coord_fixed() +
opt
plot